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Original Essays | September 15, 2014

Lois Leveen: IMG Forsooth Me Not: Shakespeare, Juliet, Her Nurse, and a Novel



There's this writer, William Shakespeare. Perhaps you've heard of him. He wrote this play, Romeo and Juliet. Maybe you've heard of it as well. It's... Continue »
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    Juliet's Nurse

    Lois Leveen 9781476757445

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Stochastic Modelling and Applied Probability #21: Stochastic Integration and Differential Equations: Version 2.1

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Stochastic Modelling and Applied Probability #21: Stochastic Integration and Differential Equations: Version 2.1 Cover

 

Synopses & Reviews

Publisher Comments:

It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach".

The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery's examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.

Synopsis:

It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emeryâ¬(tm)s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.

Table of Contents

Preliminaries.- Semimartingales and Stochastic Integrals.- Semimartingales and Decomposable Processes.- General Stochastic Integration and Local Times.- Stochastic Differential Equations.- Martingale Inequalities.- Expansion of Filtrations.- References.

Product Details

ISBN:
9783642055607
Author:
Protter, Philip E.
Publisher:
Springer
Author:
Protter, Philip
Location:
Berlin, Heidelberg
Subject:
Statistics
Subject:
Filtrations
Subject:
Lâevy processes.
Subject:
MSC (2000): 60H05, 60H10, 60H20, 60G07, 60G17, 60G44, 60G51
Subject:
Martingale representation
Subject:
Semimartingales.
Subject:
Stochastic differential equations
Subject:
Probability Theory and Stochastic Processes
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
Appl.Mathematics/Computational Methods of Engineering <P>2nd edition</P> <P>Exercises for solution added</P> <P>New topics added</P>
Subject:
Mathematics | Probability and Statistics
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Distribution (Probability theory)
Subject:
Differential equations, partial
Subject:
Engineering mathematics
Copyright:
Edition Description:
Softcover reprint of hardcover 2nd ed. 2003
Series:
Stochastic Modelling and Applied Probability
Series Volume:
21
Publication Date:
20101201
Binding:
TRADE PAPER
Language:
English
Pages:
434
Dimensions:
235 x 155 mm 652 gr

Related Subjects

Computers and Internet » Artificial Intelligence » Robotics
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Stochastic Modelling and Applied Probability #21: Stochastic Integration and Differential Equations: Version 2.1 New Trade Paper
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Product details 434 pages Springer - English 9783642055607 Reviews:
"Synopsis" by , It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emeryâ¬(tm)s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.
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